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We study the growth of an N-component (including N=1) order parameter when asystem with a Lifshitz point is quenched from the homogeneous disordered stateto the ordered states. We study the scaling behaviours of the structure factorsfor both the non-conserved and conserved order parameters in the long timelimit after a quench through the Lifshitz point by using the large-N andrenormalisation group (RG) methods. We construct the analogues of Allen-Cahnand Lifshitz-Slyzov growth laws for nonconserved and conserved order parameterswhich agree with our RG results for N=1. By extending our large-N methods tothe anisotropic Lifshitz point we show that the anisotropy is relevant for thegrowth of the nonconserved order parameter, but irrelevant for the conservedcase in the large-N limit. We discuss the effects of mode coupling terms onscaling of the structure factor for the conserved order parameter case. We alsoconsider the ordering dynamics after a quench through an off-Lifshitz point. Ina large-N set up we calculate the form of the structure factors of anon-conserved order parameter when a system is quenched from the homogeneousparamegnetic to the modulated phase. We show that after a quench from theparamegnetic to the modulated phase the form of the structure factor violatesthe standard form of dynamical scaling. Our results compare favourably with theavailable numerical results.Comment: To appear in JPhysA (2004

Scaling in a temperature quench in systems with a Lifshitz point: nonconserved and conserved order parameters